In this paper, we present an approach to generate a class of multivariate probability models, which are referred to as scale mixture of Gaussians models. They are constructed as normal variance mixture models, in which the covariance matrix involves a stochastic scale factor with a given prior distribution. We limit the presentation here to the multivariate K (MK) model, which results if we apply a Γ distribution for the scale factor. We then discuss how the parameter of the model can be estimated in an iterative procedure, and include a 2-D case study, where we compare the ability of the MK model to represent real data to corresponding abilities of the multivariate Laplace and the multivariate NIG models.